Write as a Vector Equality x+2y+4z=4 , x+y+z=0 , -x-2y+3z=3

Problem

{[x+2*y+4*z=4],[x+y+z=0],[−x−2*y+3*z=3])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the column vectors.

2. Extract the variable x from the first terms, y from the second terms, and z from the third terms to create a linear combination of vectors.

3. Set the linear combination equal to the vector formed by the constants on the right side of the equations.

4. Write the final vector equation in the form x*(v_1)+y*(v_2)+z*(v_3)=b

Final Answer

x*[[1],[1],[−1]]+y*[[2],[1],[−2]]+z*[[4],[1],[3]]=[[4],[0],[3]]

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